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We study practical data characteristics underlying federated learning, wherenon-i.i.d. data from clients have sparse features, and a certain client's localdata normally involves only a small part of the full model, called a submodel.Due to data sparsity, the classical federated averaging (FedAvg) algorithm orits variants will be severely slowed down, because when updating the globalmodel, each client's zero update of the full model excluding its submodel isinaccurately aggregated. Therefore, we propose federated submodel averaging(FedSubAvg), ensuring that the expectation of the global update of each modelparameter is equal to the average of the local updates of the clients whoinvolve it. We theoretically proved the convergence rate of FedSubAvg byderiving an upper bound under a new metric called the element-wise gradientnorm. In particular, this new metric can characterize the convergence offederated optimization over sparse data, while the conventional metric ofsquared gradient norm used in FedAvg and its variants cannot. We extensivelyevaluated FedSubAvg over both public and industrial datasets. The evaluationresults demonstrate that FedSubAvg significantly outperforms FedAvg and itsvariants.

Federated Submodel Optimization for Hot and Cold Data Features